Domestic Wind Turbines - Not That Great?

by LJ Martin

In order to reduce their carbon footprint and strive towards a carbon neutral lifestyle, a lot of people are now considering buying a small wind turbine to fix to their house. Unfortunately, the power generation from these small, domestic turbines is often very disappointing. This is due to the laws of physics, and is an unavoidable consequence of small turbine size, obstacles such as trees and buildings, and the use of turbines in parts of the world with low wind speed. This guide should help you decide whether a domestic wind turbine is right for you.

Wind turbines vary in efficiency, typically turning around 30% of the wind's power into electricity. However, we will look at the total amount of wind power which is available to the turbine, as this will show that the problems cannot be solved with improved technical designs.

The equation for the power available from the wind is this:

P = ½ ρ πr² v³

It might look a bit scary, but it's simple when you break it down.

P is the power available from the wind.ρ(Greek letter rho) is the density of the air. This varies with altitude, temperature and humidity. There's nothing much you can do about it so we will assume it's a constant in our calculations.πr² is the area of the circle swept by the turbine blades (pi times the radius squared).v³ is the wind speed cubed.

So why does this tell us that a small wind turbine bolted to the wall of your house isn't going to perform very well?

Blade diameter

First of all, let's look at the radius of the turbine blades, r. The power available is proportional to r², which means that if you double the length of the blades, there is four times more power available (2 squared = 4). In other words, a turbine of 2 metre diameter can access four times as much wind power as a 1 metre turbine. A large commercial turbine with 100 metre blade diameter is exposed to 10,000 times more wind power than a 1 metre turbine. So all things being equal, one of these enormous turbines could produce the same output as ten thousand homes with 1 metre wind turbines.

Wind speed

However, all things aren't equal, because there is an even more important variable in our equation: v³.

The wind power available to a turbine is proportional to the wind velocity cubed. In other words, doubling the wind velocity produces eight times more power (2 cubed = 8). Multiplying the wind velocity by ten results in a thousandfold increase in power. For example, a 50mph wind will produce a thousand times more power than a 5mph wind. (It seems incredible, but that's how it works.) In fact, a 50mph wind produces 37% more power than a 45mph wind. A wind turbine won't generate any electricity at all below a certain wind speed, when the power available outweighs losses due to friction and electrical resistance. This minimum wind speed varies between designs.

From this, you should realize that wind speed is absolutely crucial to the power produced by a wind turbine. Losing just a few miles per hour can dramatically reduce the amount of wind power available. So what kind of thing would reduce wind speed?

The two main things that slow the wind down are obstacles in front of the turbine and proximity to the ground. Trees, walls, houses and the ground itself will all cause the wind to slow down and swirl around, so a turbine should be placed in as exposed an area as possible. This usually means that the turbine will be on a tall pole or tower. Up there, it will be exposed to plenty of fast moving, aerodynamically "clean" air (aerodynamically "dirty" means the air is swirling around instead of moving in a nice, straight line.) Any obstacles in front of the turbine will reduce the wind power available, sometimes dramatically. You certainly don't want to bolt the turbine to a large obstacle (e.g. your house!) and preferably the turbine should not be surrounded by trees or houses. This is one reason why wind farms are usually on hills, on the coast, or out at sea.

The other consideration is whether you live in a windy area or not. If the wind speed tends to be low where you live, then even a perfectly placed turbine will not produce much electricity.

Conclusions

So what have we learned from the equation?

Firstly, small diameter turbines are much worse than large diameter ones because wind power is proportional to the area of the circle swept by the blades. Domestic wind turbines are usually around 1 metre in diameter, which strictly limits the power they can generate.

Secondly, wind speed makes a massive difference to power. If a turbine is sited on your house, any nearby trees and houses (and your own house, of course) will slow down the wind and cause it to swirl, robbing the turbine of power. If you live in a remote farmhouse on a hillside, and place a turbine on a pole away from obstacles, you can generate a respectable amount of power from a small turbine, due to the high wind speeds. However, if you live in the middle of a city, the power output may be very disappointing due to the buildings all around you slowing the wind down.

So should you buy a small, domestic wind turbine? It's your decision, but make sure you have all the facts before you take the plunge. A turbine bolted to your house will be hamstrung by its proximity to a large obstacle (the house.) A turbine in an urban environment will produce less power than an identical turbine surrounded by farmland, as buildings will obstruct the wind. Coastal and upland areas tend to have higher wind speeds. If you don't live in a windy area, it is unlikely that the turbine will produce enough power to be worthwhile.

Remember that the turbine manufacturers can only give you theoretical data on power output, as they have no way of knowing what the wind speed will be in your exact location. This has led some people, particularly in urban areas, to greatly over-estimate the amount of electricity they will generate.

Many people want to do their bit and reduce their carbon footprint, but don't rush headlong into buying a wind turbine. Make sure that you live in a windy area with an exposed place to site the turbine, and you will be able to reduce your fossil carbon emissions for years to come. If your location just isn't right for a domestic wind turbine, don't worry, there are other eco-friendly options to consider, such as solar thermal water heating, or running a car on biodiesel. Take your time, do your research and you won't end up disappointed.